A scale-dependent notion of effective dimension

Wednesday, 29 January, 2020

Published in: 

arXiv:2001.10872

We introduce a notion of "effective dimension" of a statistical model based on the number of cubes of size 1/\sqrt{n} needed to cover the model space when endowed with the Fisher Information Matrix as metric, n being the number of observations. The number of observations fixes a natural scale or resolution. The effective dimension is then measured via the spectrum of the Fisher Information Matrix regularized using this natural scale.

Author(s): 

Oksana Berezniuk
Alessio Figalli
Raffaele Ghigliazza
Kharen Musaelian